Finite Group Databasebeta

← C151×#12348 #50317273

Subgroups — C151×#12348 #50317273

Order 38656.

314 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3355×C151C211yesmaximal, characteristic, complemented
2#2244×C151C211yesmaximal, characteristic, complemented
3#2206×C151C211yesmaximal, characteristic, complemented
4#1687×C151C211yesmaximal, characteristic, complemented
5#1363×C151C211yesmaximal, characteristic, complemented
6#1333×C151C211yesmaximal, characteristic, complemented
7#1330×C151C211yesmaximal, characteristic, complemented
8#553×C151—21no—
9C2×D16×C151—21no—
10#499×C151C2211yescharacteristic
11#493×C151C2211yescharacteristic
12#482×C151—21no—
13#480×C151—21no—
14#478×C151—21no—
15#469×C151—21no—
16#459×C151—21no—
17C4×D8×C151C2211yescharacteristic
18#436×C151C2211yescharacteristic
19#428×C151—21no—
20C4⋊C16×C151C2211yescharacteristic
21#357×C151—21no—
22#357×C151—21no—
23#357×C151—21no—
24#346×C151C2211yescharacteristic
25#334×C151C2211yescharacteristic
26#331×C151—21no—
27C2×D8×C151—21no—
28C2×D8×C151—21no—
29C2×D8×C151—41no—
30C2×D8×C151D411yescharacteristic
31C2×M16×C151—21no—
32#127×C151—21no—
33#126×C151—41no—
34#125×C151—21no—
35#123×C151—41no—
36#121×C151—21no—
37#121×C151—21no—
38#121×C151—41no—
39C4×D4×C151—21no—
40C4×D4×C151—41no—
41C4×D4×C151D411yescharacteristic
42#117×C151—21no—
43C2×C4⋊C4×C151—21no—
44D16×C151—42no—
45C2×C16×C151—21no—
46C2×C16×C151—21no—
47#107×C151—21no—
48#107×C151D411yescharacteristic
49#107×C151D411yescharacteristic
50#107×C151D411yescharacteristic
51#106×C151—21no—
52#106×C151—21no—
53C4⋊C8×C151—21no—
54C4⋊C8×C151D411yescharacteristic
55#102×C151—21no—
56#102×C151—21no—
57#102×C151—21no—
58#102×C151—41no—
59C22⋊C8×C151—21no—
60C4×C8×C151C2311yescharacteristic
61C2×D4×C151—21no—
62C2×D4×C151—41no—
63C2×D4×C151—41no—
64C2×D4×C151—41no—
65C2×D4×C151—41no—
66C2×D4×C151—41no—
67C2×D4×C151D811yescharacteristic
68C22×C4×C151—21no—
69C22×C4×C151—41no—
70C22×C4×C151—41no—
71D8×C151—21no—
72D8×C151—21no—
73D8×C151—42no—
74D8×C151—41no—
75D8×C151—41no—
76D8×C151—82no—
77M16×C151—41no—
78M16×C151—41no—
79C2×C8×C151—21no—
80C2×C8×C151—41no—
81C2×C8×C151C2×D411yescharacteristic
82C2×C8×C151C2×D411yescharacteristic
83C4⋊C4×C151—21no—
84C4⋊C4×C151—21no—
85C4⋊C4×C151—21no—
86C4⋊C4×C151—41no—
87C4⋊C4×C151—41no—
88C4⋊C4×C151—41no—
89C4⋊C4×C151D811yescharacteristic
90C22⋊C4×C151—21no—
91C22⋊C4×C151—41no—
92C22⋊C4×C151—41no—
93C22⋊C4×C151—41no—
94C22⋊C4×C151—41no—
95C42×C151—41no—
96C42×C151C2×D411yescharacteristic
97C16×C151—41no—
98C16×C151—41no—
99C23×C151—21no—
100C23×C151—41no—
101C23×C151—81no—
102D4×C151—41no—
103D4×C151—41no—
104D4×C151—41no—
105D4×C151—81no—
106D4×C151—81no—
107D4×C151—82no—
108D4×C151—81no—
109D4×C151—81no—
110D4×C151—161no—
111D4×C151—161no—
112C2×C4×C151—21no—
113C2×C4×C151—41no—
114C2×C4×C151—41no—
115C2×C4×C151—41no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—161no—
119C2×C4×C151—161no—
120C2×C4×C151#12011yescharacteristic
121C2×C4×C151C2×D811yescharacteristic
122C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
123C8×C151—21no—
124C8×C151—41no—
125C8×C151—81no—
126C8×C151#13511yescharacteristic
127C8×C151AGL(1,ℤ/8)11yescharacteristic
128C22×C151—41no—
129C22×C151—41no—
130C22×C151—41no—
131C22×C151—81no—
132C22×C151—81no—
133C22×C151—81no—
134C22×C151—161no—
135C22×C151—161no—
136C22×C151—161no—
137C22×C151#44711yescharacteristic
138C4×C151—21no—
139C4×C151—21no—
140C4×C151—41no—
141C4×C151—81no—
142C4×C151—81no—
143C4×C151—81no—
144C4×C151#44911yescharacteristic
145C4×C151#45411yescharacteristic
146C2×C151—81no—
147C2×C151—161no—
148C2×C151—321no—
149C2×C151#162511yescharacteristic
150C2×C151#219011yescharacteristic
151C2×C151#219211yescharacteristic
152#12348C15111yesmaximal, characteristic, direct product factor, Sylow
153C151#1234811yescharacteristic, direct product factor, Sylow
154#3355C2×C15111yescharacteristic, complemented
155#2244C2×C15111yescharacteristic, complemented
156#2206C2×C15111yescharacteristic, complemented
157#1687C2×C15111yescharacteristic, complemented
158#1363C2×C15111yescharacteristic, complemented
159#1333C2×C15111yescharacteristic, complemented
160#1330C2×C15111yescharacteristic, complemented
161#553—21no—
162C2×D16—21no—
163#499C22×C15111yescharacteristic
164#493C22×C15111yescharacteristic
165#482—21no—
166#480—21no—
167#478—21no—
168#469—21no—
169#459—21no—
170C4×D8C22×C15111yescharacteristic
171#436C22×C15111yescharacteristic
172#428—21no—
173C4⋊C16C22×C15111yescharacteristic
174#357—21no—
175#357—21no—
176#357—21no—
177#346C22×C15111yescharacteristic
178#334C22×C15111yescharacteristic
179#331—21no—
180C2×D8—21no—
181C2×D8—21no—
182C2×D8—41no—
183C2×D8D4×C15111yescharacteristic
184C2×M16—21no—
185#127—21no—
186#126—41no—
187#125—21no—
188#123—41no—
189#121—21no—
190#121—21no—
191#121—41no—
192C4×D4—21no—
193C4×D4—41no—
194C4×D4D4×C15111yescharacteristic
195#117—21no—
196C2×C4⋊C4—21no—
197D16—42no—
198C2×C16—21no—
199C2×C16—21no—
200#107—21no—
201#107D4×C15111yescharacteristic
202#107D4×C15111yescharacteristic
203#107D4×C15111yescharacteristic
204#106—21no—
205#106—21no—
206C4⋊C8—21no—
207C4⋊C8D4×C15111yescharacteristic
208#102—21no—
209#102—21no—
210#102—21no—
211#102—41no—
212C22⋊C8—21no—
213C4×C8C23×C15111yescharacteristic
214C2×D4—21no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4D8×C15111yescharacteristic
221C22×C4—21no—
222C22×C4—41no—
223C22×C4—41no—
224D8—21no—
225D8—21no—
226D8—42no—
227D8—41no—
228D8—41no—
229D8—82no—
230M16—41no—
231M16—41no—
232C2×C8—21no—
233C2×C8—41no—
234C2×C8C2×D4×C15111yescharacteristic
235C2×C8C2×D4×C15111yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4D8×C15111yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C42—41no—
249C42C2×D4×C15111yescharacteristic
250C16—41no—
251C16—41no—
252C23—21no—
253C23—41no—
254C23—81no—
255D4—41no—
256D4—41no—
257D4—41no—
258D4—81no—
259D4—81no—
260D4—82no—
261D4—81no—
262D4—81no—
263D4—161no—
264D4—161no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—161no—
272C2×C4—161no—
273C2×C4#120×C15111yescharacteristic
274C2×C4C2×D8×C15111yescharacteristic
275C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
276C8—21no—
277C8—41no—
278C8—81no—
279C8#135×C15111yescharacteristic
280C8AGL(1,ℤ/8)×C15111yescharacteristic
281C22—41no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22—81no—
286C22—81no—
287C22—161no—
288C22—161no—
289C22—161no—
290C22#447×C15111yescharacteristic
291C4—21no—
292C4—21no—
293C4—41no—
294C4—81no—
295C4—81no—
296C4—81no—
297C4#449×C15111yescharacteristic
298C4#454×C15111yescharacteristic
299C2—81no—
300C2—161no—
301C2—321no—
302C2#1625×C15111yescharacteristic
303C2#2190×C15111yescharacteristic
304C2#2192×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC4×C8C23×C151
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ #436×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3355×C151C2semidirect
2. #2244×C151C2semidirect
3. #2206×C151C2semidirect
4. #1687×C151C2semidirect
5. #1363×C151C2semidirect
6. #1333×C151C2semidirect
7. #1330×C151C2semidirect
152. #12348C151direct (N × H)
153. C151#12348direct (N × H)
154. #3355C2×C151semidirect
155. #2244C2×C151semidirect
156. #2206C2×C151semidirect
157. #1687C2×C151semidirect
158. #1363C2×C151semidirect
159. #1333C2×C151semidirect
160. #1330C2×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3355×C1512
#2244×C1512
#2206×C1512
#1687×C1512
#1363×C1512
#1333×C1512
#1330×C1512
#12348151